China and America, we all know, are closely intertwined. Their relationship is the central faultline of the world economy. They are mutually reliant. And yet it is governed by mutual incomprehension.

Until last week, when the Financial Times saw fit to whiz me through Beijing, Shanghai and Hong Kong for a series of debates on the country's future international role, I had never set foot in mainland China. Such a whistlestop tour does not remotely qualify me to prognosticate on China's grander questions.

But the experience did ram home just how deep the differences in perceptions are between what are now the world's two most powerful countries. This could have profound implications for the world's economy, and for investors.

While FT journalists were holding polite debates, an uglier transpacific dialogue was emerging between the Chinese leadership, which in effect told the US to mind its own business when it came to China's currency, and US congressional politicians, who responded by upping pressure for their administration to declare China a currency manipulator. Such a move would pave the way for trade sanctions. Meanwhile, western investors grew ever more loudly convinced that China is in a bubble. All of these issues look different from China.

First, whatever the western perception, Chinese foreign policy is not aimed at crashing the American economy. Rather, it revolves around being left alone and around the extremely sore spot of Taiwan. Continued US weapons sales to the island, barely mentioned in the US, are seen as a deliberate and unnecessary provocation. This colours the Chinese debate on the currency.

Also, like most of us, China's leadership dislikes being told what to do. Pressure from the US for an upward revaluation is good domestic politics but reduces the chances of such a revaluation happening. Without such pressure, an appreciation would come soon.

All of this is a problem because, while China wants merely to look after its interests at home, it is so big that it cannot do so without having big effects elsewhere. The vexed issue of the currency provides the classic example.

Is China in a bubble? Generally, this is met with laughter (by Chinese and western investors alike). The answer is two-fold. First, they say, of course there are bubbles in China. Second, it does not matter.

The Shanghai stock exchange is an inefficient market driven by retail investors, where the government maintains controlling stakes in the largest players. The critical points are that investments in Shanghai stocks are not bought with borrowed money, generally, and do not account for a large chunk of the economy. It can continue its boom and bust cycle without causing great collateral damage elsewhere.

As for property prices, nobody denies that there are bubbles in the big cities. But again, the argument is that these need not have big ripple effects on the broader economy. Much of the market is fuelled with cash, while mortgages have not been resold on capital markets. A fall in property prices could not, therefore, have the disastrous economic effects that the fall in US property prices had after 2006.

China's banks will take it hard, many believe. That is a problem for the banks' shareholders, including the government. But it need not necessarily be a problem for the broader economy.

As for last year's drastic expansion of loans, which westerners fear will presage China's own domestic credit crisis, many were in effect transfers between government agencies. Nobody seems to deny that the expansion was overdone. But the Chinese view is that the government has the tools to handle the problem and still keep the economy growing nicely.

For those wanting to take a bullish long-term view on Chinese growth, the Chinese stock market is probably not the best place to do it, at least if you are interested in investing passively in an index. The stock market is simply too inefficient, and its links with the real economy too tenuous, to make this a good strategy.

An inefficient market should instead create opportunities for active investors who look for bargains and who can do some real research on the ground.

Bulls on China might instead adopt the strategy of investing in the commodities that China will need to import from overseas. Alternatively, in the long term, looking in stabler stock markets for companies that export to China might make sense.

But bulls of all descriptions should note that the vitally important economic relationship between China and the US is plagued by misunderstandings. And, of course, the widespread confidence in China might yet prove misplaced. But the view from China, at any rate, is confident.